Helen, the main point is the verb use in the context of indicating a person ‘is correct/right’ - ie avoir, not être. Avoir raison is correct speech in any level of discussion.
Just as in English, people can also have reasons - des raisons, good arguments (points) - de bons arguments or de bonnes questions etc,
As "avoir raison" -- locution verbal (elegant verbal phrase) or "raison" as noun feminine
Have a look here:
I think these links may give you the range of meanings that you are looking for.
Hope it helps.
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